I am looking for information about how different codecs function in detail. Not just the names of the containers, but what is it actually that makes one codec different from the other. Can anyone help me out with some websites or material?
That depends on what codec you are looking for/after, and what sort of level you are talking about. For example, if you do not yet have the knowledge of what these things listed below are, you are unlikely to have gains looking at those documentations.
For example, What time domain, and frequency domain are, What does it mean by direct cosine transform and fast fourier transform, What is quantization, What does it mean by quantization noise, etc.
For a good start, you can read the 'codec' wikipedia page as suggested.
Here are two example of an explanation of how mp3 works.
Tell us which of these example suits you. If even #2 is not technical enough by your standards, you should be looking at the technical standard (some of which is hosted in ISO, free of charge, others are closed). Let us know what formats you are looking for and maybe we could help more.
( Heck, We don't even know what king of codec you are looking at! Video? Audio? )
An excellent series of articles on this are Mark Pilgrim's A Gentle Introduction to Video Encoding series. Start with part 1 on Container Formats, and part 2 on video codecs and you should be on your way. The slides and presentation are also very good.